Comments on: Famous Errors?

By: PeterMcB

PeterMcB — Sun, 30 Oct 2005 17:02:11 +0000

Tongue-in-cheek, I propose the Four-Color Map Theorem, which is widely accepted as true, but is not yet proven by conventional mathematical methods. It may turn out to be false.

By: easwaran

easwaran — Sat, 29 Oct 2005 20:19:42 +0000

This was quite common up until the end of the 19th century, but I don’t know of any examples since then. In the 19th century, I know there were competing results about Fourier series (which they eventually resolved by distinguishing continuous from uniformly continuous, and convergence from uniform convergence). And I think Peano made his early career by finding counterexamples to “theorems” people had “proved”. Which is why he got interested in putting things on firmer foundations.

By: Piriki

Piriki — Sat, 29 Oct 2005 14:51:27 +0000

Dirichlet’s principle.

By: michael

michael — Sat, 29 Oct 2005 05:50:54 +0000

Salt because Lounesto is crankish? (because I never viewed him as such, although he comes acoss as self aggrandising) or that the errors aren’t all that famous?

The one that comes to mind right off the bat to me is the widely held belief way back when that continuous => differentiable, before everything was put on a firm footing.

By: sigfpe

sigfpe — Sat, 29 Oct 2005 04:44:20 +0000

Take these with a pinch of salt.